• Login
    View Item 
    •   Home
    • Theses and Dissertations
    • Theses and Dissertations
    • View Item
    •   Home
    • Theses and Dissertations
    • Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of TUScholarShareCommunitiesDateAuthorsTitlesSubjectsGenresThis CollectionDateAuthorsTitlesSubjectsGenres

    My Account

    LoginRegister

    Help

    AboutPeoplePoliciesHelp for DepositorsData DepositFAQs

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Stochastic Differential Equations: Some Risk and Insurance Applications

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    Xiong_temple_0225E_10731.pdf
    Size:
    491.8Kb
    Format:
    PDF
    Download
    Genre
    Thesis/Dissertation
    Date
    2011
    Author
    Xiong, Sheng
    Advisor
    Yang, Wei-shih, 1954-
    Committee member
    Powers, Michael R.
    Chen, Hua
    Berhanu, Shiferaw
    Department
    Mathematics
    Subject
    Mathematics
    Martingale
    Ruin Theory
    Stochastic Differential Equation
    Terrorism Risk
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/3866
    
    Metadata
    Show full item record
    DOI
    http://dx.doi.org/10.34944/dspace/3848
    Abstract
    In this dissertation, we have studied diffusion models and their applications in risk theory and insurance. Let Xt be a d-dimensional diffusion process satisfying a system of Stochastic Differential Equations defined on an open set G Rd, and let Ut be a utility function of Xt with U0 = u0. Let T be the first time that Ut reaches a level u^*. We study the Laplace transform of the distribution of T, as well as the probability of ruin, psileft(u_{0}right)=Prleft{ T<inftyright} , and other important probabilities. A class of exponential martingales is constructed to analyze the asymptotic properties of all probabilities. In addition, we prove that the expected discounted penalty function, a generalization of the probability of ultimate ruin, satisfies an elliptic partial differential equation, subject to some initial boundary conditions. Two examples from areas of actuarial work to which martingales have been applied are given to illustrate our methods and results: 1. Insurer's insolvency. 2. Terrorism risk. In particular, we study insurer's insolvency for the Cram'{e}r-Lundberg model with investments whose price follows a geometric Brownian motion. We prove the conjecture proposed by Constantinescu and Thommann.
    ADA compliance
    For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
    Collections
    Theses and Dissertations

    entitlement

     
    DSpace software (copyright © 2002 - 2023)  DuraSpace
    Temple University Libraries | 1900 N. 13th Street | Philadelphia, PA 19122
    (215) 204-8212 | scholarshare@temple.edu
    Open Repository is a service operated by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.